Question

Write an equation of the line that passes through (8,1) and is perpendicular to the line 2y+4x=12

Answer 1

`Let\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\\\\text{We have}\ k:2y+4x=12\qquad|-4x\\\\2y=-4x+12\qquad|:2\\\\y=-2x+6\to m_1=-2\\\\l:y=mx+b\to-2m=-1\qquad|:(-2)\\\\m=(1)/(2)\\\\l:y=(1)/(2)x+b\\\\\text{Put the coordinates of the point (8, 1) to the equation of the line}\ l:\\\\1=(1)/(2)(8)+b\\\\1=4+b\qquad|-4\\\\b=-3\\\\Answer:\ y=(1)/(2)x-3`